Combinatorics
* Permutation formula: \(^nP_r\) = \(\frac{n! }{ (n-r)!}\)
* Combination formula: \(^nC_r\) = \(\frac{n! }{ (r!)*(n-r)!}\)
* \(^nP_n\) = n!
* \(^nC_r\) = \(^nC_n_+_r\)
* The number of ways in which n things can be arranged taking them all at a time where p things are exactly the same,q things are exactly the same and r
things are exactly the same.
= \(\frac{n!}{p!*q!*r!}\)
* The number of ways of selecting one or more items from n given items
= \(2^n\) -1
EXTRA FORMULAS
* The number of ways of dividing (p+q) items into two groups of p & q items respectively
= \(\frac{(p+q)!}{p!*q!}\)
Probability
Probability = \(\frac{Number of favorable outcomes }{Number of all possible outcomes}\)
Probability of events A & B happening = Probability of A * Probability of B
Probability of either event A or B happening = Probability of A + Probability of B